The $(\Psi ,\Phi )$-orthogonal interpolative contractions and an application to fractional differential equations

Abstract

In this manuscript, we introduce the $(\Psi ,\Phi )$-orthogonal interpolative
contractions which generalize orthogonal interpolative contractions. We prove several fixed point theorems stating conditions under which $(\Psi ,\Phi )$-orthogonal interpolative contraction admits a fixed point. Our fixed point results are improvement of several known results in literature. As an application, we resolve a fractional differential equation.